question_answer

                         In long jumpy does it matter how high you jump? What factors determine the span of the jump?

Answer:

                Yes, in long jump, it matters how high one jumps. It is explained below. For initial velocity u and angle of projection\[\theta \], the maximum height, \[h=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\]or\[\frac{{{u}^{2}}}{g}=\frac{2h}{{{\sin }^{2}}\theta }\] and, horizontal range, \[R=\frac{{{u}^{2}}}{g}\sin 2\theta =\frac{2h}{{{\sin }^{2}}\theta }2\sin \theta \cos \theta =4h\cot \theta \] Thus the span of jump depends upon (i) height h attained (ii) angle of projection, \[\theta \].